Since the introduction of the first ring laser gyroscope (RLG) and later the fiber optic gyroscope (FOG), optical gyroscopes have become a mainstay of the global aerospace and defense industry, being used in civilian and military aircraft, rockets, and missiles for inertial navigation and varying other applications such as vehicle and antenna stabilization. Both gyroscopes operate via the Sagnac effect by which light traveling around a closed path experiences in the presence of an inertial rotation an increased optical path length when co-propagating with the rotation and a decreased path length when counter-propagating relative to the rotation. The Sagnac phase shift between light beams copropagating and counterpropagating relative to an inertial rotation Q around a closed path enclosing an area A is
      Θ    Sagnac    =            8      ⁢      π      ⁢                          ⁢      A      ⁢                          ⁢      Ω              λ      ⁢                          ⁢      σ      where λ is the optical wavelength. The phase shift can be measured as an interference pattern in the optical intensity when the two beams are combined in a FOG or as a frequency splitting of the lasing modes of the RLG.
Despite their success, RLGs and FOGs are unsuitable for many portable device applications because of their relatively large size and weight. A typical RLG weighs several kilograms with a volume exceeding 2000 cm3 and uses around 10 W of power while FOGs are only slightly better, weighing at least several hundred grams and utilizing a kilometer or more of optical fiber wrapped around a circular core with a radius 10 cm. MEMS (microelectromechanical systems) gyroscopes are miniaturized mechanical gyroscopes that can be integrated onto a standard semiconductor microchip and are used in smart phones, tablet computers, and digital cameras. However, the best MEMS gyroscopes have sensitivities that are on the order of 10 deg. per hour, which is far greater than the 0.01 deg. per hour or better sensitivities needed for inertial navigation.
Coupled resonator optical waveguides (CROWs) are arrays of circular microfabricated high-Q optical resonators originally conceived as a means of engineering the optical dispersion and group velocity of light in an integrated photonic device. CROWs are often used for optical buffering, filtering, and dispersion control in integrated optics and are routinely fabricated. The resonators are arranged into a linear array with an input waveguide that couples light into the first resonator and an output waveguide that extracts light from the final resonator of the array. The input and output coupling of the light as well as the propagation of light between resonators occurs by evanescent coupling of the electromagnetic waves between resonators. This coupling can be varied to control the optical transmission and pulse propagation velocity.
Optical Sagnac gyroscopes have used CROWs. The slow optical group velocities in CROWs were believed to lead to an enhanced sensitivity to rotations. Moreover, utilizing microresonators with radii ˜10-100 μm and N˜10-100 resonators have been made with silicon on insulator waveguides or polymer rings on silicon oxide, the overall dimensions are typically comparable to MEMS gyroscopes. It was later shown, however, that the enhanced sensitivity was a result of an improper evaluation of the sensitivity and, in reality, the sensitivity of a CROW gyroscope is equal to a resonant FOG (RFOG) with the same enclosed area. Since the sensitivity of a Sagnac gyroscope is proportional to the enclosed area and the area of a microresonator CROW gyroscope would be 105-106 times smaller than commercial FOGs, the utility of CROW gyroscopes would be quite limited. Previous proposals for CROW gyroscopes have all been based on arrays of equal size high-Q microresonators and identical evanescent coupling resulting in a periodic structure.